# Representations of set-valued risk measures defined on the $$l$$ l -tensor product of Banach lattices

Representations of set-valued risk measures defined on the $$l$$ l -tensor product of Banach... We obtain a representation for set-valued risk measures which are defined on the completed $$l$$ l -tensor product $$E\widetilde{\otimes }_l G$$ E ⊗ ~ l G of Banach lattices $$E$$ E and $$G$$ G . This representation extends known representations for set-valued risk measures defined on Bochner spaces $$L^p(\mathbb {P}, \mathbb {R}^d)$$ L p ( P , R d ) of $$p$$ p -integrable functions with values in $$\mathbb {R}^d$$ R d . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Representations of set-valued risk measures defined on the $$l$$ l -tensor product of Banach lattices

, Volume 18 (3) – Dec 18, 2013
21 pages

/lp/springer_journal/representations-of-set-valued-risk-measures-defined-on-the-l-l-tensor-IhNsa03FTB
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0267-z
Publisher site
See Article on Publisher Site

### Abstract

We obtain a representation for set-valued risk measures which are defined on the completed $$l$$ l -tensor product $$E\widetilde{\otimes }_l G$$ E ⊗ ~ l G of Banach lattices $$E$$ E and $$G$$ G . This representation extends known representations for set-valued risk measures defined on Bochner spaces $$L^p(\mathbb {P}, \mathbb {R}^d)$$ L p ( P , R d ) of $$p$$ p -integrable functions with values in $$\mathbb {R}^d$$ R d .

### Journal

PositivitySpringer Journals

Published: Dec 18, 2013

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